A powerful car bomb exploded on a busy street in Christian East Beirut today, killing at least 60 people and injuring nearly 200 as the blast collapsed apartment building walls and set dozens of cars afire, police reported. There was no indication who was responsible or what the target was.

Among those killed were 15 children in a school bus incinerated by a wall of flame that swept down the street.

On Beirut's southern edges, battles between Shiite Moslem militiamen and Palestinians for control of three major refugee camps continued for a third day, with reports of Shiite advances into at least two of the camps and accounts by hospital sources of Shiite gunmen attacking wounded Palestinians in hospitals and preventing their treatment.

The car bomb exploded in a section of the Sin el Fil district crowded with low income and refugee Christian families. The blast occurred about 1 1/2 miles from the private residence of President Amin Gemayel, but it was not known whether that had been the target.

St. Elias Street, the scene of the explosion, was a blackened mass of twisted iron, smoking cars and bodies. The front and back walls of two high-rise buildings and the facade of another collapsed from the intensity of the blast and the balconies of nearby apartment buildings were blown out. Motorists were seen trapped in burning cars and pedestrians were pinned under slabs of concrete and debris.

In the spreading battle for the Sabra, Shatila and Burj al Barajinah refugee camps, Palestinian forces led by Col. Abu Musa used positions in the hills overlooking Beirut from the east to shell Shiite districts and access routes to lift pressure off the besieged camps.

The Shiite militia, the country's strongest Moslem military force, wants to prevent the Palestinians from turning the Beirut camps and southern Lebanon into their own strongholds, as they were before the Israeli invasion in 1982. The Shiites say this could draw Israeli reprisals against their villages.

At least 34 people were killed and 160 wounded in the fighting in and around the camps today, police reported, bringing the total since Sunday to more than 150 known dead and at least 800 wounded.

Security sources in Amal, the Shiite militia, said both the Sabra and Shatila camps had fallen, but Palestinians in the camps told reporters that only sections of the camps had been overrun by Amal and troops of the Lebanese Army's 6th Brigade. The 6th Brigade, while part of the regular Army, is a predominantly Shiite unit that has been sympathetic to Amal throughout the sectarian fighting.

Amal militiamen herded jeeploads of blindfolded Palestinians, apparently captured in Sabra and Shatila, to the Shiites' main interrogation center in the 40-story Murr Tower in Beirut, The Associated Press reported. Militiamen in battle fatigues pushed their prisoners into the building, slapping and beating them, according to reporters outside the building. The militiamen barred photographers from taking pictures.

At a hospital in Moslem west Beirut, sources who begged anonymity said Amal gunmen forced their way to the wards and gunned down a number of Palestinians being treated for serious injuries.

At the American University of Beirut hospital, Shiite fighters prevented ambulances from unloading wounded Palestinians at the emergency room for treatment.

The International Committee of the Red Cross made one brief entry at dawn into Sabra but its convoys had to retreat after coming under gunfire by Shiite militiamen.

The three days of fighting between the Shiite militia and the Palestinians have left previous political alliances unclear.

The Palestinian fighters include both those still loyal to Yasser Arafat and pro-Syrians such as Abu Musa who bitterly oppose Arafat's leadership of the Palestine Liberation Organization.

The Shiites have long been allied with Syria and the Lebanese Druze militia, but there has been no evidence of direct Syrian or Druze involvement in the current fighting.

A group of Sunni Moslem leaders appealed today to Syrian President Hafez Assad to intervene and put a halt to the violence. Druze leader Walid Jumblatt, a one-time ally of Amal leader Nabih Berri, went to Damascus to confer with Syrian leaders on the crisis.

Arafat, according to aides in Amman, called for intervention by the U.N. Security Council to stop "treacherous aggression" against refugees in the camps.

But the official Syrian news agency accused Arafat of masterminding the battle to distract Amal from its struggle against Israel and to punish Palestinians who allied themselves with Syria.

The Christian militia radio said Jumblatt told reporters in Damascus that Palestinians should be in control of their own camps. The Moslem-controlled Lebanese television, which is openly sympathetic to Amal, said an agreement was being drawn in Damascus for collective supervision of the camps by Amal, the Lebanese Army's 6th Brigade and pro-Syrian Palestinians.

Rumors about the possible deployment of Syrian troops in Lebanon and a reported desire by Damascus to cut down to size militias that have grown too large and unruly for Syria to control added to confusion here over the Syrian role.